RKKY coupling in graphene

Abstract

We study the carrier-mediated exchange interaction, the so-called RKKY coupling, between two magnetic moments in graphene using exact diagonalization on the honeycomb lattice. By using the tight-binding nearest neighbor band structure of graphene we avoid the use of a momentum cut-off which plagues results in the Dirac continuum model formulation. We extract both the short and long impurity-impurity distance behavior and show several corrections to earlier long distance results. In the bulk the RKKY coupling is proportional to $1/|\mathbf{R}{|}^3$ and displays $(1+\cos (2{\mathbf{k}}_D\cdot \mathbf{R})$-type oscillations. A-A sublattice coupling is always ferromagnetic whereas A-B subattice coupling is always antiferromagnetic and three times as large. We also study the effect of edges in zigzag graphene nanoribbons (ZGNRs) and find that for impurities on the edge, the RKKY coupling decays exponentially because of the localized zero energy edge states. For impurities inside a ZGNR the bulk characteristics are quickly regained.

8 pages, 6 figures

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• Analytical Expression for the RKKY Interaction in Doped Graphene
• Carbon nanotubes in electric and magnetic fields
• Discovery of Weyl nodal lines in a single-layer ferromagnet
• RKKY interaction in carbon nanotubes and graphene nanoribbons
• RKKY interaction on the surface of three-dimensional Dirac semimetals
• Ruderman-Kittel-Kasuya-Yosida interaction in Weyl semimetals
• The importance of electron-electron interactions in the RKKY coupling in graphene
• Indirect exchange interaction between magnetic adatoms in a monolayer MoS2
• Topological phase and edge states dependence of the RKKY interaction in zigzag silicene nanoribbon
• Dynamic RKKY interaction in graphene
• Effect of Rashba splitting on RKKY interaction in topological insulator thin films
• Antiferromagnetic nuclear spin helix and topological superconductivity in ${}^{13}$C nanotubes
• Fractionalized Fermi liquids and exotic superconductivity in the Kitaev-Kondo lattice
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• Electronic structure of graphene beyond the linear dispersion regime
• RKKY Interaction in Disordered Graphene
• RKKY interaction in a doped pseudospin-1 fermion system at finite temperature
• RKKY Interactions in Graphene: Dependence on Disorder and Gate Voltage
• Fingerprints of tilted Dirac cones on the RKKY exchange interaction in 8-Pmmn Borophene
• Lateral Interfaces of Transition Metal Dichalcogenides: A Stable Tunable One-Dimensional Physics Platform
• Ruderman-Kittel-Kasuya-Yosida interaction in biased bilayer graphene
• Gate-Tunable Exchange Coupling Between Cobalt Clusters on Graphene
• Block Lanczos density-matrix renormalization group method for general Anderson impurity models: Application to magnetic impurity problems in graphene
• RKKY interaction between adsorbed magnetic impurities in graphene: symmetry and strain effects
• RKKY interaction in gapped or doped graphene
• Probing the edge states in a zigzag phosphorene nanoribbon via RKKY exchange interaction
• Noncollinear twisted RKKY interaction on the optically driven SnTe(001) surface
• Non-Equilibrium RKKY Interaction in Irradiated Graphene
• Engineering spin exchange in non-bipartite graphene zigzag edges
• Effective magnetic correlations in hole-doped graphene nanoflakes
• Stabilization of magnetic skyrmions by RKKY interactions
• RKKY interaction and intervalley processes in p-doped transition metal dichalcogenides
• Indirect RKKY interaction in armchair graphene nanoribbons
• Defect Induced Resonances and Magnetic Patterns in Graphene
• Properties of single-layer graphene doped by nitrogen with different concentrations
• Strain-induced modulation of magnetic interactions in graphene
• Effect of magnetic field and chemical potential on the RKKY interaction in the $\alpha$-${\mathcal{T}}_3$ lattice
• Magnetization profile for impurities in graphene nanoribbons
• Magnetoplasmons for the $\alpha$-T${}_3$ model with filled Landau levels
• Macroscopic Degeneracy and Emergent Frustration in a Honeycomb Lattice Magnet
• Gap-modulated doping effects on indirect exchange interaction between magnetic impurities in graphene
• Focusing RKKY interaction by graphene P-N junction
• Indirect coupling between localized magnetic moments in triangular graphene nanoflakes
• Symmetries and hybridization in the indirect interaction between magnetic moments in MoS${}_2$ nanoflakes
• Probing topological phases in a perturbed Kane-Mele model via RKKY interaction: Application to monolayer jacutingaite Pt${}_2$HgSe${}_3$
• RKKY interaction in bilayer graphene
• Long-range exchange interaction between magnetic impurities in graphene
• Signature of gate-tunable magnetism in graphene grafted with Pt-porphyrins
• Interlayer RKKY Coupling in Bulk Rashba Semiconductors under Topological Phase Transition
• RKKY interaction between extended magnetic defect lines in graphene
• Modulation of Kekulé adatom ordering due to strain in graphene
• Noncollinear exchange interaction in transition metal dichalcogenide edges
• RKKY Interactions in Graphene Landau Levels
• Gate-tunable magnetism of C adatoms on graphene
• Spin-spin correlations of magnetic impurities in graphene
• Ferromagnetism in chiral multilayer 2D semimetals
• Indirect exchange interaction between magnetic adatoms in graphene
• Long range of indirect exchange interaction on the edges of MoS${}_2$ flakes
• Indirect exchange of magnetic impurities in zigzag graphene ribbon
• Weak ferromagnetism of antiferromagnetic domains in graphene with defects
• Signatures of interfacial topological chiral modes via RKKY exchange interaction in Dirac and Weyl systems
• Yu-Shiba-Rusinov States and Ordering of Magnetic Impurities Near the Boundary of a Superconducting Nanowire
• Magnetic exchange mechanism for electronic gap opening in graphene
• Theory of Vacancy-Induced Intrinsic Magnetic Impurity with Quasi-Localized Spin Moment in Graphene
• MN4 Embedded Graphene Layers: Tunable Decay Rate of RKKY Interaction
• Potential and spin-exchange interaction between Anderson impurities in graphene
• Kondo effect due to a hydrogen impurity in graphene: a multichannel Kondo problem with diverging hybridization
• Impurity States and Indirect Exchange Interaction in Irradiated Graphene
• Non-local control of spin-spin correlation in finite geometry helical edge
• RKKY interaction in heavily vacant graphene
• Competing long-range interactions and spin vector chirality in spin-chains
• Critical temperature of two-dimensional hydrogenated multilayer graphene-based diluted ferromagnet
• Anisotropic RKKY interactions mediated by $j=3/2$ quasiparticles in half-Heusler topological semimetal
• Boltzmann conductivity of ferromagnetic graphene with magnetic impurities
• RKKY interaction in one-dimensional flat-band lattices
• On the Sign of Fermion-Mediated Interactions
• An Origin of Dzyaloshinskii-Moriya Interaction at Graphene-Ferromagnet Interfaces Due to the Intralayer RKKY/BR Interaction
• Spin Stiffness and Domain Walls in Dirac-Electron Mediated Magnets
• Dynamic RKKY interaction between magnetic moments in graphene nanoribbons
• RKKY plateau in zero- and one-dimensional triangular Kagome lattice models
• RKKY interaction in a spin-split superconductor
• RKKY interaction at helical edges of topological superconductors
• Magnetic order through Kondo coupling to quantum spin liquids
• RKKY interaction in graphene at finite temperature
• Zitterbewegung-mediated RKKY coupling in topological insulator thin films
• The effect of midgap states on the magnetic exchange interaction mediated by a $d$-wave superconductor
• Indirect coupling between localized magnetic moments in zero-dimensional graphene nanostructures (quantum dots)
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• Influence of flat bands on RKKY interaction: perspective of Fano defects
• Numerical package for QFT calculations of defect-induced phenomena in graphene
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• Long-Range Order and Quantum Criticality in Antiferromagnetic Chains with Long-Range Staggered Interactions